Villaretq0
2022-06-27
Answered

How can I prove ${\mathrm{\Sigma}}_{i=1}^{n-1}i={(}_{2}^{n})$

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asked 2020-11-09

Use proof by Contradiction to prove that the sum of an irrational number and a rational number is irrational.

asked 2021-08-02

Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B.

a) the set of sophomores taking discrete mathematics in your school

b) the set of sophomores at your school who are not taking discrete mathematics

c) the set of students at your school who either are sophomores or are taking discrete mathematics

Use these symbols:$\cap \cup$

a) the set of sophomores taking discrete mathematics in your school

b) the set of sophomores at your school who are not taking discrete mathematics

c) the set of students at your school who either are sophomores or are taking discrete mathematics

Use these symbols:

asked 2021-07-28

Let A, B, and C be sets. Show that

asked 2021-08-18

Discrete Mathematics Basics

1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where$(a,b)\in R$ if and only if

I) everyone who has visited Web page a has also visited Web page b.

II) there are no common links found on both Web page a and Web page b.

III) there is at least one common link on Web page a and Web page b.

1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where

I) everyone who has visited Web page a has also visited Web page b.

II) there are no common links found on both Web page a and Web page b.

III) there is at least one common link on Web page a and Web page b.

asked 2021-08-22

Find the number of edges in a circulant graph Circ$[n,\{k,l\}]$ . In mathematica you can explore these graphs by using the comand CirculantGraph $[n,\{k,l\}$ .

asked 2022-05-14

(Solved)Find the number of 9 letter words using the letters P, Q, and R containing at least one P and at least two Qs.

Please help me with the last question on my discrete maths assignment because I can't get what I am doing wrong.

Find the number of 9 letter words using the letters P, Q, and R containing at least one P and at least two Qs.

number of 9 letter words that use all 3 letters $={3}^{9}$.

${A}_{1}=$ number of 9 letter words without the use of P $={2}^{9}$

${A}_{2}=$ number of 9 letter words without the use of Q $={2}^{9}$

${A}_{3}=$ number of 9 letter words using at least 1 Q $={3}^{9}-{2}^{9}$.

${A}_{1}\cap {A}_{2}={1}^{9}$

${A}_{1}\cap {A}_{3}={2}^{9}-1$

${A}_{2}\cap {A}_{3}=0$

${A}_{1}\cap {A}_{2}\cap {A}_{3}=0$

number of words using at least 1 P and at least 2 Qs

$={3}^{9}-({2}^{9}+{2}^{9}+({3}^{9}-{2}^{9})-(1+{2}^{9}-1-0)+0)=0$

I can't understand where I am making a mistake because everything seems to make sense.

Please help me with the last question on my discrete maths assignment because I can't get what I am doing wrong.

Find the number of 9 letter words using the letters P, Q, and R containing at least one P and at least two Qs.

number of 9 letter words that use all 3 letters $={3}^{9}$.

${A}_{1}=$ number of 9 letter words without the use of P $={2}^{9}$

${A}_{2}=$ number of 9 letter words without the use of Q $={2}^{9}$

${A}_{3}=$ number of 9 letter words using at least 1 Q $={3}^{9}-{2}^{9}$.

${A}_{1}\cap {A}_{2}={1}^{9}$

${A}_{1}\cap {A}_{3}={2}^{9}-1$

${A}_{2}\cap {A}_{3}=0$

${A}_{1}\cap {A}_{2}\cap {A}_{3}=0$

number of words using at least 1 P and at least 2 Qs

$={3}^{9}-({2}^{9}+{2}^{9}+({3}^{9}-{2}^{9})-(1+{2}^{9}-1-0)+0)=0$

I can't understand where I am making a mistake because everything seems to make sense.

asked 2022-04-16

How many strings are there of lowercase letters of length four or less, not counting the empty string?